The president’s approval ratings matched all-time lows ahead of Sunday night’s dramatic announcement that U.S. special-operations forces had stormed a compound near Islamabad and killed the terrorist behind the Sept. 11, 2001 attacks.

On Monday, Obama basked in bipartisan praise that included compliments from former Vice President Dick Cheney. Networks continued to broadcast images from the night before, when crowds of young students chanting, “USA” celebrated bin Laden’s death outside the president’s front door.

Obama said the “world is safer” with bin Laden dead, and that “this is a good day for America.”

He will travel to Ground Zero in New York City on Thursday.

To be sure, it is still a long way until November 2012, and the economy remains the dominant political issue for the White House and congressional Republicans alike.

Yet the idea Obama had picked up a huge trump card in directing a mission that killed his country’s most notorious enemy was reflected in the smiles and good moods of White House staff on Monday.

At the White House press briefing, officials played up Obama’s decisiveness in making the call to send U.S. forces into a compound in Pakistan without that country’s knowledge.

Counterterrorism chief John Brennan praised his boss, calling it “one of the most gutsiest calls of any president in recent memory” and making sure reporters knew who deserved the credit.

“The president made the decision. And the results, I think, speak for themselves,” Brennan said.

Jubilant White House officials declined to speak about the political ramifications of killing bin Laden, but most in — and outside — the building seemed to agree that Obama’s anemic poll numbers were about to get a sizable bump.

“I would anticipate, based on history, that Obama’s job approval rating will increase further in the wake of Sunday night’s announcement,” Gallup’s editor in chief, Frank Newport, wrote on Monday.

But just how big of a bounce Obama gets, and how long it will last, is more difficult to predict.

President George W. Bush’s sky-high numbers in the aftermath of the 9/11 attacks eventually fell back to earth, while his father, President George H.W. Bush, enjoyed such a boost in his approval ratings following the 1991 Gulf War that many observers thought he was virtually invincible in his 1992 reelection effort.

Instead, the senior Bush failed to win reelection just a year and a half after the end of the Gulf War, largely because of voter unhappiness with the state of the economy.

Officials made it clear that the White House believes the president, who has been criticized in the past for being indecisive, now has a powerful story to tell about his decisiveness and leadership on national security. A candidate criticized in 2008 for not being experienced enough to take the 3 a.m. national-security call has now directed a mission that resulted in the death of bin Laden.

Despite the aura of exhilaration at the White House, observers warned that Obama’s reelection is far from assured as voters return their focus to the economy.

Lara Brown, a political science professor at Villanova University, said that “while the news of Osama’s death is a positive and important development for our country and for the president, its beneficial effect on Americans’ mood and the president’s poll numbers is likely to be ephemeral.”

The reason, she said, is voter fixation on the economy.

“It is likely that [Obama] will enjoy a temporary rise in his poll numbers and a possible reappraisal from voters for his competency as commander in chief acting and directing foreign affairs,” Brown said. “Still, these assessments will, not unlike the continuing military conflicts, be balanced against the voters’ economic concerns, like high unemployment, slow growth, high gas prices and large budget deficits.”

Simmons acknowledged that “the economy is still phenomenally important” in determining Obama’s political future.

“But killing Osama and literally feeding his body to the sharks helps make a strong case to moderate voters in North Carolina, Arizona, Nevada and central Florida that this president can defend this nation and should be allowed to keep doing so,” Simmons said.

Short- and long-term challenges now await the president.

Because bin Laden was buried at sea, the White House is coming under pressure to release pictures of the slain terrorist to dispel conspiracy theories.

“We are going to do everything we can to make sure that nobody has any basis to try to deny that we got Osama bin Laden,” said Brennan, though whether photos are to be released is still being determined.

Some Democrats are already using bin Laden’s death as a rationale for a complete withdrawal of troops from Afghanistan, even as Obama and his top military aides have warned that progress there, while consistent, remains fragile and reversible.